Problem: Find the greatest common factor of $35$ and $20$.
The greatest common factor (GCF) is the largest number that is a factor of both $35$ and $20$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}35 &=5\cdot7\\\\\\\\ 20&=2\cdot2\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}35 &=5\cdot7\\\\\\\\ 20&=2\cdot2\cdot5 \end{aligned}$ Each number shares the factor ${5}$, so the GCF is ${5}$. The greatest common factor of $35$ and $20$ is $5$.